Finite Group Databasebeta

← #119527

Subgroups — #119527

Order 512.

660 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21820C211yesmaximal, characteristic
2C2×#1805C211yesmaximal, characteristic
3C2×#1491C211yesmaximal, characteristic
4#8033C211yesmaximal, characteristic
5C2×#1290C211yesmaximal, characteristic
6C2×#1283C211yesmaximal, characteristic
7#7914C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×#103C412yes—
14C2×C4×M16C2211yescharacteristic
15C2×#382C2211yescharacteristic
16#1985—22no—
17#1984—21no—
18#1984—21no—
19#1817—22no—
20#1805—21no—
21#1805—21no—
22#1805—21no—
23#1805—21no—
24C2×#340C412yes—
25#1491—22no—
26#1491—22no—
27C2×Q8⋊C8—21no—
28C2×Q8⋊C8—21no—
29#1295—22no—
30#1290—22no—
31#1283—22no—
32#1280—22no—
33C23×Q8C2×C411yescharacteristic
34C22×M16—21no—
35C23×C8C2×C412yes—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8D411yescharacteristic
47C2×C4×Q8D411yescharacteristic
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8D411yescharacteristic
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C412yes—
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432D412yes—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×#103—22no—
77C2×#103—22no—
78C2×#103—44no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8D412yes—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16D412yes—
86C2×#97—21no—
87C2×#97—21no—
88C2×#97D412yes—
89C2×C4×C8—21no—
90C2×C4×C8—21no—
91#382—21no—
92#382—21no—
93#382—21no—
94#382—21no—
95C2×#95—21no—
96C2×#95—21no—
97#340—22no—
98#340—22no—
99#336—24no—
100#336—24no—
101Q8⋊C8—24no—
102Q8⋊C8—24no—
103C22×Q8—21no—
104C22×Q8—22no—
105C22×Q8—22no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8C22⋊C411yescharacteristic
113C22×Q8C22⋊C411yescharacteristic
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—22no—
117C23×C4C22×C411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4#4111yescharacteristic
120C2×M16—24no—
121C2×M16—22no—
122C2×M16—42no—
123C2×M16—41no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8—42no—
132C22×C8—42no—
133C4×Q8—21no—
134C4×Q8—21no—
135C4×Q8—21no—
136C4×Q8—21no—
137C4×Q8—21no—
138C4×Q8—21no—
139C4×Q8—21no—
140C4×Q8—21no—
141C4×Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144C4×Q8—21no—
145C4×Q8—21no—
146C4×Q8—21no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4C22⋊C411yescharacteristic
175C2×C4⋊C4C22⋊C411yescharacteristic
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42—41no—
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42#4111yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206#103—44no—
207#103—44no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C22⋊C8—41no—
212C22⋊C8—41no—
213C22⋊C8—41no—
214#97—22no—
215#97—22no—
216#97—22no—
217#97—22no—
218#97—41no—
219#97—41no—
220C4×C8—22no—
221C4×C8—41no—
222C4×C8—41no—
223C4×C8—41no—
224#95—41no—
225#95—41no—
226#95—41no—
227#95—41no—
228C24C4×D411yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8#10012yes—
252C2×Q8#10112yes—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—82no—
276C22×C4—82no—
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4#11711yescharacteristic
279C22×C4#11711yescharacteristic
280C22×C4C4×D411yescharacteristic
281C22×C4C4×D411yescharacteristic
282C22×C4C4×D411yescharacteristic
283C22×C4#12011yescharacteristic
284C22×C4#12111yescharacteristic
285C22×C4#12111yescharacteristic
286C22×C4#12111yescharacteristic
287C22×C4#12111yescharacteristic
288C22×C4#12311yescharacteristic
289C22×C4#12311yescharacteristic
290C22×C4#12311yescharacteristic
291C22×C4#12411yescharacteristic
292C22×C4#12411yescharacteristic
293C22×C4#12611yescharacteristic
294C22×C4#12611yescharacteristic
295M16—24no—
296M16—44no—
297M16—42no—
298C2×C8—44no—
299C2×C8—42no—
300C2×C8—44no—
301C2×C8—44no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—82no—
309C2×C8—82no—
310C2×C8—82no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—82no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42#12011yescharacteristic
337C42#12111yescharacteristic
338C42#12111yescharacteristic
339C42#12111yescharacteristic
340C42#12111yescharacteristic
341C42#12311yescharacteristic
342C42#12311yescharacteristic
343C42#12311yescharacteristic
344C42#12311yescharacteristic
345C42#12311yescharacteristic
346C42#12311yescharacteristic
347C42#12311yescharacteristic
348C42#12411yescharacteristic
349C42#12411yescharacteristic
350C42#12611yescharacteristic
351C42#12611yescharacteristic
352C23—21no—
353C23—21no—
354C23—22no—
355C23#38611yescharacteristic
356C23#38811yescharacteristic
357C23#38811yescharacteristic
358C23#44312yes—
359C23#44412yes—
360Q8—22no—
361Q8—22no—
362Q8—22no—
363Q8—22no—
364Q8—44no—
365Q8—44no—
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—82no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—162no—
413C2×C4—162no—
414C2×C4#38111yescharacteristic
415C2×C4#38611yescharacteristic
416C2×C4#38811yescharacteristic
417C2×C4#38811yescharacteristic
418C2×C4#39411yescharacteristic
419C2×C4#39411yescharacteristic
420C2×C4#39411yescharacteristic
421C2×C4#39411yescharacteristic
422C2×C4#39711yescharacteristic
423C2×C4#39711yescharacteristic
424C2×C4#39711yescharacteristic
425C2×C4#39711yescharacteristic
426C2×C4C2×#10011yescharacteristic
427C2×C4C2×#10111yescharacteristic
428C2×C4#41311yescharacteristic
429C2×C4#41311yescharacteristic
430C8—44no—
431C8—82no—
432C8—82no—
433C8—82no—
434C8—82no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22#144011yescharacteristic
444C22#187612yes—
445C22#190011yescharacteristic
446C22#190111yescharacteristic
447C22#190512yes—
448C22#192912yes—
449C22#193711yescharacteristic
450C22#193811yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—81no—
464C4—81no—
465C4—162no—
466C4#182111yescharacteristic
467C4#182211yescharacteristic
468C4#190011yescharacteristic
469C4#190111yescharacteristic
470C2—22no—
471C2—21no—
472C2—21no—
473C2#924412yes—
474C2#924612yes—
475C2#1118411yescharacteristic
476C2#1119111yescharacteristic
477C2#1119811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#218202
C2×#18052
C2×#14912
#80332
C2×#12902
C2×#12832
#79142